Ann. Limnol. - Int. J. Lim. 51 (2015) 37–47 Ó EDP Sciences, 2015 DOI: 10.1051/limn/2014030
Available online at: www.limnology-journal.org
A simplified algorithm for calculating benthic nutrient fluxes in river systems Gilles Billen1*, Josette Garnier1 and Marie Silvestre2 1 2
UMR Sisyphe, UPMC/CNRS, 4 place Jussieu, 75005 Paris, France FR FIRE, UPMC/CNRS, 4 place Jussieu, 75005 Paris, France Received 19 October 2013; Accepted 24 September 2014 Abstract – Benthic organic matter microbial oxidation is the basic process by which oxidants such as oxygen, nitrate and sulphate are consumed in sediments, while ammonium and phosphate are released. Although these processes play a crucial role in river biogeochemistry, their modelling remains a difficult challenge. Thouvenot et al. [J. Hydrol., 341, 55–78, 2007; 379, 239–250, 2009] have proposed a model of the processes involved in organic matter degradation in a vertical gradient of oxic to anoxic conditions, considering one upper fluid, erodable sediment layer, with transient behaviour, overlaying a compacted sediment layer assumed to be at steady state. In this paper, we present a thorough analysis of the response of Thouvenot’s model to the various constraints affecting benthic processes, according to a conceptual interpretative framework relating the nutrient fluxes across the sediment–water interface to the depth-integrated value of certain sediment properties, such as their oxidant demand and their total ammonification rate. Based on this analysis, we propose a new alternative algorithm simplifying the calculation of the benthic fluxes. This algorithm is designed to be suitable for inclusion in any model of in-stream biogeochemical processes. Key words: Benthic processes / nutrient cycling / river systems / modelling
Introduction In aquatic systems, including river systems, the benthic boundary layer (Lorke and MacIntyre, 2009) represents a hot spot of biological and biogeochemical processes. Benthic fluxes indeed play a significant role of transformation, retention and elimination of nutrients from the water column (Garnier and Billen, 1993; Seitzinger et al., 2002). In shallow, small order rivers, the benthic compartment, in addition to being the site of deposited sediment reworking, might also be defined as the hyporheic zone, i.e., the area where stream water mixes with shallow groundwater (Runkel et al., 2003). Hyporheic exchanges, or movement of surface water into and out of the streambed, increases the volume of stream water in contact with sediment biota, enhancing biologic reactions. These are particularly important in rivers flowing over gravel beds, where the interaction between biofilms and hyporheic flow (Sa´nchezPe´rez et al., 2003; Weng et al., 2003; Flipo et al., 2004; Peyrard et al., 2011) plays a major role, besides the direct interaction of bottom sediments with the overlying river water. In most lowland rivers, however, as well as in lentic *Corresponding author:
[email protected]
systems, benthic processes are dominated by the diffusive exchange of solutes between the water column and a layer of freshly deposited, re-erodable and compacting sediments (Billen and Lancelot, 1988). High hyporheic advective fluxes, as reported by Sheibley et al. (2003), are rather exceptional in this context, but the stream flow, and its variations, are enhancing the exchanges between the freshly deposited particles and the water column. The properties of these sediments, in particular their content in biodegradable organic matter, are the main drivers of oxygen and nutrient exchanges across the water–sediment interface (Arndt et al., 2013). Experimental approaches to benthic nutrient exchanges have been reviewed by Viollier et al. (2003); they include direct measurements using bell-jars (Billen et al., 1989; Garban et al., 1995) or measurements of gradients using cores, dialysis cells (Garban et al., 1995) or microelectrodes (Dedieu et al., 2007). Based on data from these types of measurement, a number of models of benthic fluxes have been proposed, relating the flux of sedimenting organic material to consumption of oxygen and production of nutrients in the benthos compartment. Soetaert et al. (2000) have reviewed the published approaches to couple benthic and water column biogeochemical models.
Article published by EDP Sciences
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G. Billen et al.: Ann. Limnol. - Int. J. Lim. 51 (2015) 37–47
a. Analytical diagenetic models (Berner,1980; Boudreau, 1997) Steady state diagenesis assumed
SS Water column Compacting sediment
sedim
SED
Nuts diffusive fluxes
b. Multi-layer numerical approach
c. Two layers hybrid approach
(e.g.Soetaert et al., 1996) Transient states considered
(Thouvenot et al., 2007, 2009) Transient state in the upper fluid layer Steady state in the lower layer
SS Water column
Nuts diffusive fluxes
sedim
Multi-layer sediment
SED SED
Water column Fluid benthic layer
SED Compactd sediment layer
SS erosion sedim
Nuts diffusive fluxes
SED compaction
Fig. 1. A simplified typology of nutrient–benthic–nutrient remineralization models.
The first generation of models used to describe benthic processes are those developed by Berner and Aller in the 1980s and early 1990s, assuming steady-state conditions and analytically solving simple diagenetic equations (Vanderborght et al., 1977; Lerman, 1978; Berner, 1980; Westrich and Berner, 1984; Aller and Aller, 1992) (Fig. 1(a)). Other authors in the 1990s introduced numerical models considering vertically resolved discrete layers of sediments able to take into account the fine depth resolution of benthic processes as well as their transient nature (Rabouille and Gaillard, 1991; Boudreau, 1996, 1997; Soetaert et al., 1996; Testa et al., 2013) (Fig. 1(b)). When applied to rivers, this strategy leads to either oversimplified approaches with only one or two sediment layers for each river stretch (Even et al., 2007) or very high calculation costs. More recently, Thouvenot et al. (2007, 2009) have proposed a hybrid approach considering one upper fluid, erodable sediment layer, with transient behaviour, overlaying a compacted sediment layer assumed to be at steady state (Fig. 1(c)). The model is based on a detailed analysis of the processes involved in organic matter degradation in a vertical gradient of oxic to anoxic conditions. Contrary to the multi-layer approaches, the model makes the choice, for the lower compacted layer, of an analytical resolution of the diagenetic equations instead of numerical modelling. Thouvenot’s model has been implemented in the current version of the Seneque/ Riverstrahler model describing biogeochemical processes in drainage networks (Ruelland et al., 2007; Thieu et al., 2009) and validated with direct measurements available in the Seine river system (Thouvenot et al., 2009). However, the calculation scheme associated with this model, based on the analytical resolution of diagenetic equations, is numerically complex, because it requires solving implicit equations, making this benthic module of the Seneque/Riverstrahler model rather expensive in terms of calculation time. Moreover, this part of the calculation scheme has been found to be unstable in certain extreme modelling situations. In this paper, we present a thorough analysis of the response of Thouvenot’s model to the various constraints
affecting benthic processes, primarily based on the concept of oxidant benthic demand, which we argue is the major driver of all benthic processes, as also discussed in detail by the recent review published by Arndt et al. (2013). Based on this analysis, we propose a new alternative algorithm simplifying the calculation of the benthic fluxes, while complying with the constraint of matter conservation. The algorithm is designed to be suitable for inclusion in any model of in-stream biogeochemical processes, including Seneque/Riverstrahler, but also other modelling approaches such as SWAT (Arnold et al., 1998, 1999).
Experimental basis for the concept of benthic oxidant demand Benthic organic matter microbial oxidation is the basic process by which oxidants such as oxygen, nitrate and sulphate are consumed in sediments, while ammonium and phosphate are released. The organic matter content of the upper layers of sediments is therefore a logical proxy for the intensity of benthic processes. Most of the organic matter pool of sediments is, however, of very low biodegradability so that a similar total content of organic matter between two sediment samples may mask large differences in rapidly biodegradable organic matter fractions, hence in overall reactivity.
Methods
Benthic organic matter reactivity can be better characterized by measuring the associated oxygen consumption rate over a short period of time in a sediment slurry under oxic conditions (potential oxygen consumption) or by measuring nitrate consumption under anoxic conditions with added nitrate at a saturating concentration (potential denitrification rate) (Garnier et al., 2010). In the latter case, the measured rate corresponds to the oxidant demand of the organic matter degradation by the
G. Billen et al.: Ann. Limnol. - Int. J. Lim. 51 (2015) 37–47
denitrifying microbial population present. In the former case, the measured oxygen consumption rate corresponds to the sum of the oxidant demand of the organic carbon biodegradable by the aerobic heterotrophic microbial community present and of the nitrification rate of the simultaneously released ammonium. By following in parallel the nitrate production rate, both the carbon and the nitrogen oxidant demand can be estimated (Fig. 2(a)). Such measurements were carried out with 25 sediment samples collected in different stream-order rivers of the Seine drainage network, both upstream and downstream from the Paris urban agglomeration. Integration of the time variation curve of oxygen consumption, the denitrification rate under anoxic conditions and the ammonium production rate made it possible to determine the total oxidant demand under oxic and anoxic conditions as well as the total biodegradable organic C and N initially present in the sample.
Results
Total biodegradable organic N was found to be closely related to biodegradable organic C (Fig. 2(b)), as was the instant ammonification rate (not shown). Another remarkable result of these measurements is that the total C oxidant demand is similarly related to biodegradable organic C in oxic and anoxic conditions (Fig. 2(c)). This supports the view that intrinsic organic carbon degradability controls both aerobic respiration and heterotrophic denitrification by adapted communities of heterotrophic microorganisms. The data are consistent with the view that benthic organic material comprises three classes of biodegradability, a rapidly degradable fraction (with degradation constant k1 of about 0.005 hx1 at 20 xC), a slowly biodegradable fraction (k2 = 0.00025 hx1) and a third fraction which can be considered refractory over a yearly time span, as was postulated by the formalism of the model proposed by Thouvenot et al. (2007, 2009).
Thouvenot’s model of nutrient water column–benthic exchanges The model reported by Thouvenot et al. (2007, 2009) considers an upper layer of freshly deposited, uncompacted material, which can be re-eroded, and is assumed to be homogeneous in terms of the distribution of particulate properties, overlaying a lower layer of consolidated, stratified sediments. Molecular diffusion prevails in the compacted lower layer, while mixing coefficient is five times higher in the upper layer. Organic matter of three classes of biodegradability is brought into the upper layer by sedimentation from the water column, mixed with inorganic particulate material, and degraded there, according to their respective first-order biodegradability rate. If not re-eroded, they are compacting into the lower layer.
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The model calculates the vertical distribution of dissolved oxygen and nutrients in the two sedimentary layers, taking into account the processes of ammonification, nitrification and denitrification, adsorption of ammonium and phosphate onto particulate material, as well as the resulting fluxes of dissolved species across the water–sediment interface (Fig. 3). The basis for this calculation is the solving of the diagenetic equations for oxygen, inorganic nitrogen and phosphorus species and dissolved silica, assuming a steady-state dissolved compartment. When implemented into a river basin model (e.g., the Riverstrahler model), the river model provides, for each river stretch at any time step, the boundary conditions to the diagenetic benthic module, namely the value of all water-quality variables in the water column and all benthic particulate variables in the upper fluid layer, including the particulate organic matter concentration of all biodegradability classes, inorganic particulate material and depth of the fluid layer. The benthic module calculates the steadystate sediment–water fluxes resulting from these varying conditions. The model has been validated in its local version with benthic chamber measurements of nutrient fluxes and nutrient analysis in the pore water of sediment cores collected at the same sites (Thouvenot et al., 2007) and in its river network version with measurements of sediment properties along the entire river network, including biodegradable organic matter concentration in the top sediment layer, denitrification potential and benthic chamber oxygen, ammonium and nitrate flux determinations (Thouvenot et al., 2009).
A re-analysis of Thouvenot’s model results By systematically exploring the response of the model to varying values of the control variables of Thouvenot’s model, we aim at providing a simpler algorithm to replace the original model, thus constructing a surrogate model (or metamodel) of the original one. This purpose is often achieved by standard multivariate blind statistical analysis of the results of a large number of runs of the model with a random choice of control variables. Tool kits for such operations are available (Gorissen et al., 2010). Following this approach, Gypens et al. (2008), following exactly the same purpose as we do in this paper, made use of MonteCarlo simulations with an analytical two-layer diagenesis model to statistically derived multiple linear equations that best describes the model results. This kind of approach, however, generally results in losing the basic understanding of the mechanistic relationships which are at the basis of the original model. We preferred instead to analyse the results according to a conceptual interpretative framework relating the nutrient fluxes across the sediment–water interface to the depthintegrated value of certain sediment properties, such as their oxidant demand and their total ammonification rate. Doing so, we not only establish empirical relationships between nutrient fluxes and state variables calculated by
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G. Billen et al.: Ann. Limnol. - Int. J. Lim. 51 (2015) 37–47
a. Bottom sediments from 25 sites in the Seine drainage network
Sediment slurry
Sediment slurry
subsamples
4h
0
4h
NO3 (mgN.l–1)
4h
Biodegradable orgN
0
denitrification rate 0 0
5 months
b. Rate of ammonification proportional to C biodegradation
C oxidant demand under anoxic cond. 0
4h
tot biodegradable N (mgN.g–1)
0 0
5 months
Nminr rate (mgN.l–1.h–1)
0 0
4h
NO3 (mgN.l–1)
N2
0 0
denit rate (mgN.l–1.h–1)
Anoxic conditions
NO3 (mgN.l–1)
4h
N mineralization rate 0 0
O2 cons rate (mg.l–1.h–1)
O2 consumption rate 0 0
O2
O2 (mg.l–1)
O2 (mg.l–1)
5 months incubation under oxic conditions
NO3 (mgN.l–1)
Oxic conditions
O2
5 months
0.8
y = 0.20x 2
R = 0.95
0.6
0.4
0.2
0.0 0
anoxic Coxid demand (µeq.g–1.h–1)
C oxidant demand (µeq.g–1.h–1)
oxic anoxic
3.0
2.0
1.0
0.0 0
1
2
tot biodegradable C (mgC.g–1)
3
1
2
3
4
tot biodegradable C (mgC.g–1)
c. The rate of oxidant consumption, as oxygen in aerobiosis or as nitrate (denitrification) under anoxic conditions, is similarly related to biodegradable orgC. 100.00
10.00
1.00
0.10
0.01 0.01
0.10
1.00
10.00
100.00
oxic C oxidant demand (µeq.g–1.h–1)
Fig. 2. (a) Experimental measurements of organic matter mineralization in sediment slurries under aerobic and anaerobic conditions. (b) Relationships between ammonification rate and organic matter degradation and between oxic and anoxic oxidant demand and biodegradable organic C content of sediments.
NH4
NO3
41
O2
HP3 HP1,2 N2
Df >> Dc
FlNH4 nitrif
HB3 HB1,2
Dc = molecular diffusion
Compacted sediment layer
Fluid benthic layer
Water column
G. Billen et al.: Ann. Limnol. - Int. J. Lim. 51 (2015) 37–47
NH4
FlNO3 NO3
FlO2 oxic layer anoxic layer
NO3
comp HB1,2
limit of O2 penetration
limit of NO3 penetration
NH4 denit
Fig. 3. State variables and processes taken into account in Thouvenot’s model of benthic nutrient recycling.
Ammonium benthic flux
Ammonium release from the benthos can be considered a fraction of the steady-state depth-integrated ammonification rate, Ammonr. This can be expressed as the sum of the ammonification rate of the biodegradable fractions of organic matter present in the upper fluid benthic layer and of the flux of biodegradable organic nitrogen compacted into the lower sediment layer, where it will be degraded over the long run. According to the hypotheses of Thouvenot’s model, this can be expressed as: Ammonr ðgN:m2 :h1 Þ ¼ 1=ðc=nÞ ðk1 HB1 þ k2 HB2Þ þ comp ðHB1 þ HB2Þ=ðc=nÞ
with
comp ¼ 0 if SED
